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Answers by Dr. Jonathan Y.

Find the limit? (answer)

lim    (sin(x+h)-sin(x))/h h→0 since sin(x+h) = sin(x) cos(h) + cos(x) sin(h)    then we have   lim   (sin(x) cos(h) + cos(x) sin(h) - sin(x))/h h→0  grouping 1st and 3rd term, we have     lim...

Solve the equation. (answer)

Beautiful work by Vivian L. of Middletown, CT!   Student also needs to know the strategy of solution this type of equation.   Step 1:  square both side.   (or arrange into this format if it is given differently)   Step 2: rearrange to format...

is 15/17 more or less than 1? (answer)

To compare two fractions, use the following method: 15             1 17             1                     multiply first numerator with second denominator and put the result...

Why do some children have difficulty with rotational symmetry? (answer)

Rotational Symmetry is part of Group Theory. For HS STEM subjects, rotational symmetry is often introduced using 2D figures or 3D objects. I believe ALL, I mean all, children can understand and eventually master rotational symmetry by practicing with figures and objects with n-fold rotational...

x+3y=7, find the y-intercept (answer)

Arrange the equation in the slope-intercept format:   y = mx + b  --------------- eq. 1                    where b is the intercept.  Given:    x+3y=7  Rearrange it:     3y=-x + 7  ...

how to show work for algebra proportions. (answer)

Math is Fun! Once you get the "algebra proportion" from the wonderful tutors Krista B., and Diane S., you can make math fun, like: Knowing that some other people call this "equivalent fraction". Let's think about the following question: Use ALL the nine digits,...